Question

A wooden stool is in the form of a frustum of a cone with slant edge 40cm,top diameter 30cm and bottom diameter 50cm.

1. calculate the perpendicular height of the stool
2. calculate the total surface area of the stool in terms of π  
3. calculate the volume of wood used to make the stool in terms of
4. given that the density of the wood used to make the stool is 0.8g/cm³, calculate the mass of the stool in kg

Answer 1

1. 
   
   15 =    L   
   25    L+40
   15L + 600 = 25L
     L=60cm
     H=√(100² − 25²) =96.82cm
   96.82 =100
      h        60
         h = 58.09cm
   Perpendicular height = 96.82−58.09
                                   = 38.73
2. Base = πr² =625π
   Top   =       =225π
   C.S.A=πRL − πrl
           =2500π − 900π = 1600π
   T.S.A = 2450π
3. v=¹/₃ × 625π × 96.82 − ¹/₃ × 225π × 58.09
    =20170.8π − 4356.75π = 15814.05π
4. M=v × d
     = 15814.05 × 3.143 × 0.8
                  1000
     =39.76kg